4.
(05.05 HC)
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Part A:
To find the height of the base, we need to use the formula for the volume of a triangular prism:
Volume = (1/2) * base * height * length
Plugging in the values we know:
1,200 = (1/2) * 10 * h * 20
1,200 = 100h
h = 1,200 / 100 = 12 cm
Therefore, the height of the base is 12 cm.
Part B:
To find the amount of cardboard used to make the candy box, we need to calculate the surface area of the triangular prism. The surface area of a triangular prism can be calculated by finding the area of the two triangular bases and the three rectangular faces and adding them together.
Area of a triangular base = (1/2) * base * height
Area of one triangular base = (1/2) * 10 * 12 = 60 cm^2
Area of both triangular bases = 2 * 60 = 120 cm^2
Area of a rectangular face = base * height
Area of one rectangular face = 10 * 20 = 200 cm^2
Area of all three rectangular faces = 3 * 200 = 600 cm^2
Total surface area = 120 + 600 = 720 cm^2
Therefore, approximately 720 square centimeters of cardboard would be used to make the candy box.